25686 ÷ 7 = 3669 R3
Alright, let's work through the division of 25686 by 7 step by step.

Step 1:
7 goes into 2 0 times with a remainder of 2.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 2 to get 2.
Bring next digit (5) of the dividend behind the 2 and repeat the process: 25 / 7

Step 2:
7 goes into 25 3 times with a remainder of 4.
Write down 3 as next digit of of the result. 
Result so far: 3
Subtract 21 from 25 to get 4.
Bring next digit (6) of the dividend behind the 4 and repeat the process: 46 / 7

Step 3:
7 goes into 46 6 times with a remainder of 4.
Write down 6 as next digit of of the result. 
Result so far: 36
Subtract 42 from 46 to get 4.
Bring next digit (8) of the dividend behind the 4 and repeat the process: 48 / 7

Step 4:
7 goes into 48 6 times with a remainder of 6.
Write down 6 as next digit of of the result. 
Result so far: 366
Subtract 42 from 48 to get 6.
Bring next digit (6) of the dividend behind the 6 and repeat the process: 66 / 7

Step 5:
7 goes into 66 9 times with a remainder of 3.
Write down 9 as next digit of of the result. 
Result so far: 3669
Subtract 63 from 66 to get 3.

The final result is 3669 with a remainder of 3.